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## #26 2013-09-21 05:45:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

That makes sure there are 4 different types and removes duplicates.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #27 2013-09-21 05:48:26

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

But, there aren't 4 types of pens.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #28 2013-09-21 05:50:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

Yes there is, type 1,2,3, and 4. They are the second number in each list.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #29 2013-09-21 05:53:05

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

Nowhere in the problem is stated that we can't choose both red1 and green1. That is the main problem with the definition of ans2.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #30 2013-09-21 05:54:50

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

Here is a code that gets the correct answer

``````s = {{r, 1}, {r, 2}, {b, 1}, {b, 2}, {b, 3}, {g, 1}, {g, 2}, {g, 3}, {g, 4}};
ans = Permutations[s, {4}];
ans1 = Select[ans, Length[Union[#[[All, 1]]]] == 3 &];
ans2 = Union[Sort /@ ans1] // Length``````

Last edited by anonimnystefy (2013-09-21 05:55:02)

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #31 2013-09-21 05:58:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

Okay, let me try that.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #32 2013-09-21 05:59:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

I have noticed it is pretty much the same as yours except it doesn't have the ans2 line.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #33 2013-09-21 06:01:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

How does it deal with this part?

You want to purchase 4 pens, each of a different type

Where is that condition done?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #34 2013-09-21 06:05:08

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

It's the ans1 line, which is the same as yours.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #35 2013-09-21 06:07:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

But if the second numbers are the types, this one only has 2 different types, not 4.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #36 2013-09-21 06:08:51

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

Those numbers are used just for differentiating the pens.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #37 2013-09-21 06:14:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

I think you are correct but I do not agree with the problem wording. It is my major dislike of that site.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #38 2013-09-21 06:17:04

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

If the problem with this problem's wording is that it says type, you should know type refers to the colour.

What the problem with that site is, is most of the problems are user submitted and probably not very much checked.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #39 2013-09-21 06:19:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

That is where I did not get that idea and came up with a different answer.
Luckily this was not in my problem set.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #40 2013-09-21 11:45:42

bob bundy
Registered: 2010-06-20
Posts: 8,629

### Re: Combinatorics

I have a complete list.  I used my method of post 2, eliminating repeats.  There are 72.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #41 2013-09-21 11:47:37

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

144?

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #42 2013-09-21 11:52:04

bob bundy
Registered: 2010-06-20
Posts: 8,629

### Re: Combinatorics

No 72.  I just re-read the question and took out the repeated types.

It's just 24 x 6 divided by 2.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #43 2013-09-21 12:00:01

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

Ah, okay.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #44 2013-09-21 14:32:21

bob bundy
Registered: 2010-06-20
Posts: 8,629

### Re: Combinatorics

Here they are:

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #45 2013-09-21 15:14:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,861
Website

### Re: Combinatorics

I don't really understand how GFs are used. Could anyone teach me?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #46 2013-09-21 20:51:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

You asked that question in the other forum that we are both members of. I believe it was about partitions.

Generating functions are a way to change a combinatorics problem into a computational one. What would you like to do with them?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #47 2013-09-21 22:55:15

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,861
Website

### Re: Combinatorics

this problem.

stefy's forum? I've lost the link

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #48 2013-09-21 22:59:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Combinatorics

http://maths.freeforums.org/

Did you expand his gf?

http://www.mathisfunforum.com/viewtopic … 87#p268687

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #49 2013-09-22 02:07:01

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,861
Website

### Re: Combinatorics

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #50 2013-09-22 02:16:43

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Combinatorics

Hi Agnishom

You can also check out this thread: http://www.mathisfunforum.com/viewtopic … =17704&p=2.  Bobbym gave some interesting examples in that thread which use GFs like I did for the problem in this thread.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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